National political reporter

Foreign Minister Julie Bishop has asked her department to work with the Attorney-General and Immigration departments to come up with a federal government response to the case of baby Gammy.

Ms Bishop said the three departments were ''considering what response the Australian government should provide'' to the ''tragic situation''.

''We're looking at it from every angle, in terms of foreign affairs, immigration and the Attorney-General's office,'' she told reporters in Canberra on Tuesday.

This comes after Fairfax Media reported that an Australian couple had abandoned their baby boy, who was born with Down Syndrome in Thailand to a surrogate mother.

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Prime Minister Tony Abbott described the situation as ''tragic''.

''I don't think there would be anyone in the country who wouldn't be really pretty cut up about what's happening here,'' he said.

''There are no easy answers when it comes to government, when it comes to institutional arrangements. For me, the one shining light to come from this most unfortunate, deeply regrettable situation is that there appears to be an absolute outpouring of generosity towards baby Gammy and his mother.''

An inter-departmental committee met for the first time on Monday and it is understood it will look at both particular issues in the case of Gammy and broader issues relating the international commercial surrogacy.

The government has previously noted that the regulation of surrogacy is a matter for states and territories.